For point clouds, the CD [1]} and EMD [2]} are the most suitable cost functions.
CD tries to find the minimum distance between two sets of points, i.e., in our case the ground truth and the estimated point clouds.
In the following, let the ground truth point cloud be \( X_{p} \)  and the network output be \( \widehat{X}_{p} \) .
The CD is defined as:
\( \begin{split}d_{cd}(\widehat{X}_{p}, X_{p}) = \sum _{x \in \widehat{X}_{p}} \underset{y \in X_{p}}{min} \left\Vert  x - y \right\Vert _{2}^{2} \\+ \sum _{y \in X_{p}} \underset{x \in \widehat{X}_{p}}{min} \left\Vert  x - y \right\Vert _{2}^{2}\end{split}\) 
